Question 1125748: I am stuck on this problem, can someone assist me please? Thank you.
Most nutritionists now agree that a healthy adult diet should include 25−35 g of fiber each day. A breakfast of 2 blueberry muffins, 1 banana, and a 1-cup serving of cereal contains 15 g of fiber; a breakfast of 1 blueberry muffin, 2 bananas, and a 1-cup serving of cereal contains 17.5 g of fiber; and a breakfast of
2 blueberry muffins and a 1-cup serving of cereal contains 10 g of fiber. How much fiber is in each of these foods?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let x = the number of grams of fiber in a blueberry muffin.
let y = the number of grams of fiber in a banana.
let z= the number of grams of fiber in a serving of cereal.
your equations become:
2x + y + z = 15
x + 2y + z = 17.5
2x + 0y + z = 10
these 3 equations need to be solved simultaneously.
take the first 2 equations and solve for x and y by eliminating z.
you get:
2x + y + z = 15
x + 2y + z = 17.5
subtract the second equation form the first to get x - y = -2.5
take the second and third equatioon and solve for x and y by eliminating z.
2x + y + z = 15
2x + 0y + z = 10
subtract the second equation from the first to get y = 5.
go back to the equation of x - y = -2.5 and replace y with 5 to get:
x - 5 = -2.5
add 5 to both sides of this equation to get x = 2.5
you now have x = 2.5 and y = 5.
go back to the first original equation of 2x + y + z = 15 and replace x with 2.5 and y with 5 to get 5 + 5 + z = 15 which results in z = 5.
your values are:
x = 2.5
y = 5
z = 5
evaluate all 3 original equations to see that they are true when you use these values for x,y,z.
the 3 original equations are:
2x + y + z = 15 which becomes 2*2.5 + 5 + 5 = 15 which becomes 15 = 15.
x + 2y + z = 17.5 which becomes 2.5 + 10 + 5 = 17.5 which becomes 17.5 = 17.5.
2x + 0y + z = 10 which becomes 2*2.5 + 5 = 10 which becomes 10 = 10.
all 3 equations are true, therefore the solution is good.
the solution is:
there are 2.5 grams of fiber in a blueberry muffin.
there are 5 grams of fiber in a banana.
there are 5 grams of fiber in a serving of cereal.
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